Short answer: yes, you can (and they've been allowed for some time). IIRC, the rules for shadar-kai as PCs come from a Dragon
article, and, as per the Campaign Guide
, all Dragon
content (except for Unearthed Arcana
articles) is legal in LFR.
Just to note: these particular message boards are an old, "legacy" forum, a leftover from the period before WotC rebuilt the forums into the "Wizards Community", and created a separate group (and forum) for LFR. As a legacy forum, this set of message boards sees very little traffic (as the VCL for the RPGA, I come back here every couple of days, just to see if anyone's stumbled in here by mistake).
The new LFR boards see quite a bit of traffic, and are regularly monitored by the LFR campaign staff. You can find them here:community.wizards.com/lfr/go/forum/viewb...
(Note that you may need to ask to become a member of the LFR group before you can post on those boards.)
Hope this helps!
"Of course [Richard] has a knife. He always has a knife. We all have knives. It's 1183, and we're barbarians!" - Eleanor of Aquitaine, "The Lion in Winter"